Question

calculate ratio of the area to volume for unit cube, a unit sphere inscribed inside the cube and as right cylinder inscribed inside the cube

Answer 1

sphere diameter is the side of the cube, so radius is 1/2.

cylinder diameter and height are the side of the cube, so r = 1/2, h=1

cube: v=1 a=6, so 6:1
sphere: v=4/3 pi (1/2)^3 = pi/6
a = 4pi(1/2)^2 = pi
so, 6:1

cylinder: v = pi (1/2)^2 = pi/4
area= pi/2 + 2pi(1/2)(1) = 3pi/2
so, 6:1

whoda thunk it?

Answer 2

a cone is inscribed in a hemisphere which is inscribed inside a cylinder. show that the ratio of the volumes of cone to hemisphere to cylinder is 1:2:3